In her annual report the general manager of a car rental business observes that commercial bookings constituted 32 per cent of the bookings received over the previous year. Out of a random sample of 146 bookings received for the current year, 40 are commercial bookings. Test the hypothesis that the proportion of commercial bookings in the current year is at least as high as the proportion received last year using a 5 per cent level of significance.

The mean weight of the cabin baggage checked in by a random sample of 40 passengers at an international airport departure terminal was 3.47 kilograms. The sample standard deviation was 0.82 kilogram. Construct a 90 per cent confidence interval for the mean weight of cabin baggage checked in by passengers at the terminal.

2. A company is introducing a job evaluation scheme in which all jobs are graded by points for skill, responsibility and so on. Monthly pay scales (RS in 1000's) are then drawn up according to the number of points allocated and other factors such as experience and local conditions. The company has applied this scheme to 9 jobs:
Job I II III IV V VI VII VIII IX
Points 5 25 7 19 10 12 15 28 16
Pay 3 5 3.25 6.5 5.5 5.6 6 7.2 6.1

Find the least squares regression line for linking pay scales to points.

Estimate the monthly pay for a job graded by 18 points.

3. A sample of 20 production workers in a company earned the following net pay amounts after all deductions for a given week: 240, 240, 240, 240, 240, 240, 240, 255, 255, 265, 265, 280, 280, 290, 300, 305, 325, 330, 340. Calculate the

mean,

median and

mode for this group of wages.

4. The weekly sales of two products A and B were recorded as given below:

Product A 59 75 27 63 27 28 56
Product B 150 200 125 310 330 250 225

Find out which of the two shows greater fluctuation in sales.

5. A garage offers a breakdown recovery service for motorists that is available every day of the year. According to their records the number of call-outs they received per day last year were:

Number of Call-outs 0 1 2 3 4
Number of days 68 103 145 37 12

What is the probability that they receive:

two call-outs in a day?

more than two call-outs in a day?

6. Chief Executive Officer of a life insurance company wants to undertake a survey of the huge number of insurance policies that the company has underwritten. The company makes yearly profit on each policy that is distributed with mean 8000 and standard deviation 300. It is desired that the survey must be large enough to reduce the standard error to no more than 1.5 per cent of the population mean. How large should sample be?

7. An auto company decided to introduce a new six cylinder car whose mean petrol consumption is claimed to be lower than that of the existing auto engine. It was found that the mean petrol consumption for 80 cars was 12 km per litre with a standard deviation of 4.5 km per litre. Test the claim of the company, that the new car petrol consumption is 10 km per litre on the average at 5 per cent level significance.

8. What do you mean by correlation and regression? Explain how these concepts are used in forecasting of business data.

9. Define the following:

Bivariate Data

Pairwise Independence of Events

Bernoulli Process

Sampling Distribution

Confidence Level

Efficiency of an Estimator

Coefficient of Determination